- Abelian groups, solvable and nilpotent groups,
- permutation groups and linear groups,
- Mathieu groups,
- Frattini and Fitting groups,
- extensions of groups,
- free groups and presentations.
Group Theory (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-40-17-M-7||Group Theory||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||56 h||214 h||-||-||PL1||9.0||irreg.|
- About [MAT-40-17-K-7]: Title: "Group Theory"; Presence-Time: 56 h; Self-Study: 214 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 84170 ("Group Theory")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Upon successful completion of the module, the students know and understand the basic principles and methods of the theory of finite groups. They have studied important examples of finite groups and are able to examine those using scientific methods. They are able to name the main propositions of the lecture, classify and explain the illustrated relationships. They understand the proofs and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.
By completing exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the lecture.
- B. Huppert: Endliche Gruppen I,
- H. Kurzweil: Endliche Gruppen,
- D. Gorenstein: Finite Groups.
Requirements for attendance (informal)
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-22-K-3] Introduction to Algebra (2V+1U, 4.5 LP)
Requirements for attendance (formal)